Performance on WHO data.

<p>novelTest.ext denotes our test based on extreme paths, dcor distance covariance and hoeffd Hoeffding's D. All methods were applied to all comparison between pairwise variables which had Pearson's product moment correlation coefficient near zero to exclude linear relationships. Only pairwise complete observations were used as most methods cannot handle missing vallues. All comparisons include ate least 81 datapoints. In total we compare all 3 methods on 2971 variable pairs.</p

Benchmark of all methods.

<p>cor denotes Pearson's product moment correlation coefficient, dcor distance covariance, hoeffd Hoeffding's D, MIC denotes MIC, novelTest.chisq is our test based on Pearson's test and novelTest.ext is our test based on extreme paths. Each plot shows the power (on the y-axis) against the MI (x-axis). We examine 8 different types of dependence: linear, quadratic, cubic, sine with period , , circle, step function and the dependence called "patchwork copula'' (<b>A–H</b>)</p

Diagrams explaining Equations 1 and 2 for , and (panel A) and (panel B) with the reference point at coordinates .

<p><b>A</b>: We define 3 regions I, II and III (black, red and blue points respectively). Region I has the least number of constraints and the number of admissible configurations is the number of possibilities to draw points from positions without replacement nor ordering: . The number of admissible configurations for region II is given by the number of rows available and the number of columns which remain to be filled according to . Region III has the remaining points freely distributed, yielding admissible configurations. <b>B</b>: In the case we add an additional region of points exactly at distance (green points). There can be such points. Region I has size and admissible configurations with the number of points strictly inside the square of distance . Region IIa and IIb are symmetric and handled analogous to region II in panel A with and . Region III has admissible configurations analogous to panel A.</p